Question

point v lies between points u and w on uw. if uw = 9x - 9, what is uw in units? 5 units 6 units 30 units 36 units

Explanation:

Step1: Use segment addition postulate

Since \(UV + VW=UW\), we have \((2x - 4)+(4x + 10)=9x - 9\).

Step2: Simplify the left - hand side

Combine like terms: \(2x-4 + 4x+10=6x + 6\). So, \(6x+6 = 9x-9\).

Step3: Solve for \(x\)

Subtract \(6x\) from both sides: \(6=3x - 9\). Add \(9\) to both sides: \(15 = 3x\). Divide by \(3\): \(x = 5\).

Step4: Find \(UW\)

Substitute \(x = 5\) into \(UW=9x - 9\). Then \(UW=9\times5-9=45 - 9=36\).

Answer:

36 units